The motor drive circuit is working! Here's a snapshot of the setup. I can easily control the speed using the arduino sketch. The DRV8825 gets very hot during operation so I'll need to make sure I am heatsinking that properly. 

I also created a small lever arm for the motor and installed it in the egg with some weights (quarters). The egg did wobble when I ran the motor which is a good sign but I need to make some adjustments to improve it:

• Decrease weight and thickness of egg vessel. I'd like to go down to 3mm for the walls. 
• Eliminate the threads of the egg vessel and move to fasteners to reduce weight.
• Decrease motor weight or increase weight on the lever. I need to do some more research here to figure this part out. The nema-17 motor is pretty heavy and makes it difficult to shift the center of gravity of the egg without a massive counter weight.

Next Steps: 

• Improve 3D printed egg
• Add boost converter to breadboard so I can power everything with a single voltage supply (4.7V).